Archive for January, 2018

The Mathematics Of Euclid
The Greek Maths legend – Euclid is known throughout history as among the greatest mathematicians and in fact one of his names is the father of geometry. You might not be aware that the standard geometry all people are taught in college is actually called Euclidian Geometry. In Ancient Greece, he worked tirelessly and Euclid accumulated all the knowledge developed in mathematics during that time. From his studies he created his famous work, entitled ‘The Elements’. It is thought that Euclid likely attended Plato’s academy in Athens before moving into Alexandria, in Egypt. In this time, the city had a big library and whats more it even had ready access to papyrus made it the centre for the productions of books. The papyrus is one of the numerous reasons why excellent minds such as Heron of Alexandria and Euclid established themselves in Alexandria and the Nile delta.

Nowadays Euclid, is even more famous and his books and theorems are an essential part of any mathematics education. You’ll find him studied at every levels from elementary to I last saw a copy in Dublin, in the University College.

Euclid’s Elements consisted of thirteen novels covering a vast body of mathematical expertise, crossing arithmetic, geometry and number theory. The fundamental arrangement of the components starts with Euclid launching axioms. From here he created 465 propositions, progressing from his first recognized principles into the unknown in several of measures, a process he called the Artificial strategy. He looked at mathematics as a whole, but was especially focused on geometry and this specific field formed the foundation of his work. Euclid’s Axioms were based upon 10 statements which could be accepted as mathematical truths. He named these axioms his postulates and split them into two groups of five, these very first set common to all math, the second specific to geometry.

To see some great explanations of these geometric principles search through YouTube or the Open University Maths lessons. These were recently broadcast on the BBC so you can pick them up on iPlayer – this post shows how to pick up BBC iPlayer from Ireland but it should work from anywhere in the world too.

Many of those postulates appear into be self explanatory into us, but Euclid worked on the principle that no axiom might be accepted without proof. Euclid’s First Group of Postulates – these Common Notions: Things that are equal to these same thing are equal to one another. If equals are added onto equals, the results are equal. If equals are subtracted from equals, these remains are equal. Things which coincide with one another are equal to one another. A straight line can be drawn between any two points.

Any finite straight line can be extended indefinitely in a straight line. For any line segment, it’s potential to draw a circle utilizing the section as these radius and one end point as these centre. If a straight line falling across two other straight lines leads to these sum of these angles on these same side less than two right angles, then these two straight lines. These lines if extended indefinitely, meet on these same side as these side where these angle amounts are less than two right angles.

Euclid felt that anyone who can read and comprehend words could comprehend his notions and postulates but, into make sure, he included 23 definitions of common words, like point and line to ensure that there might be no semantic errors.

Carl Friedrich Gauss was a dominant figure in 19th century Germany primarily because of his accomplishments in the field of mathematics. He’s famous for his monumental contribution to data, algebra, differential geometry, mechanics, astronomy and other mathematical theories among many other fields. Those Individuals who respect his work very frequently refer to him as the greatest mathematician who ever lived and in Latin this is known as the Princeps mathematicorum.

Johann Carl Friedrich Gauss was born 30 Apr 1777 from the Duchy of Brunswick from a lower class illiterate family. His mother actually didn’t record his birth date as she lacked the education to do so. In fact he had to work out his own age by figuring his birthday by himself taking traces from the times she associated with his arrival.

There’s no doubt about that the young Gauss was a prodigy from a very early age, many noticed his remarkable intellect. He was a mathematically precocious kid that he proved it over and over again. Indeed still as a teenager, he made many landmark mathematical discoveries. By the age of 21, Gauss had already wrote his magnum opus which is entitled the Disquisitiones Arithmeticae. This work of his basically altered the landscape of number theory from the years and is still utilized until this day.

The local ruler soon recognised his potential and was to become Gauss’s patron. The Duke of Brunswick found his work impressive and made a decision to send him into the Collegium Carolinum. He attended the college in the early 1790s while he studied in the University of Guttingen during the latter part of the decade. This part of his life was covered beautifully in a documentary series created by the BBC about famous mathematicians. If it’s still available, you might find it on the BBC iPlayer site although you’ll need to buy a UK VPN or proxy like this if you’re outside the UK.

During his studies he discovered many new theorems and transformed existing ones into a brand new functions. He created a groundbreaking discovery in 1796 which explained how a polygon can be assembled by the item of unique Fermat primes and using the power of 2. Turns out it was this gigantic discovery in the arena of mathematics that made Gauss into choosing mathematics as his main career instead of philology. Indeed Gauss made mathematics a very important part of his life right up until his death. He actually chose that his tombstone is into be inscribed with heptadecagon that was created by a local stonemason with great difficulty. Gauss embarked upon a brand new voyage with this new development in 1796. His another key work in maths was the development of number theory.

He simplified manipulations in quantity theory by making progress in modular arithmetic. Quadratic reciprocity law was demonstrated by him the same year, rendering him the first man into accomplish the task. Furthermore, he conjectured the prime quantity theorem which allows also a deeper understanding into the distribution of the prime numbers into the integers. Additionally to these self made discoveries and the many improvements to standard theories, he also collaborated with the physics professor Wilhelm Weber in 1831. They worked on the project of magnetism and came up with the representative unity of mass, time and charge.

In addition to magnetism, they made unique findings at Kirchhoffs circuit laws at electricity. They initiated the first electromechanical telegraph, connecting the institute because of physics in Gottingen with the observatory. One of Gauss’s most important and noteworthy publications is the Dioptrische Untersuchungen which was published in 1840.

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